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40^4 ^I I

GPL' , 1TIONAL-WAVE BURSTS FROM THE NUCLEI OF DISTANT GALAXLFS AND QUASARS: *+ PRGPOSAL FOR DETECTION USING DOPPLER TRACKING OF INTERPLANETARY SPACECRAFT

KIP S. THORNE

Californi,% Ints_itute of Technology, Pasadena, California, U.S.A.

and

VLADIMIR B. BRAGINSKY

1 1 hystcs Faculty, Moscow State University, Moscow, U.S.S.R.

(NASA-CR-145432) GRAVITATIONAL-WAVE BURSTS N76-10977 FROM THE NUCLEI OF DISTANT GALLXIES AND QUASARS: PROPOSAL FOR DETECTION USING 6 J^ DOPPLER TRACKING OF INTERPLANETARY Unclas SPACFCRAFT (California Inst. of Tech.) 17 p G3/93 39447 R p v19 5 Nq4 41

Supported in part by the Ministry of Higher Education, U.S.S.R.; and by the

National Aeronau and Space Administration [NCR-05-002-2561 and the

National Science Foundation [MPS75-013981, U.S.A.

Based in part on lectures by V. B. Braginsky at Caltech, Stanford, L.S.U., M.I.T.,

and Princeton in October 1974, and by K. S. 'Thorne at the Symposium on Theoretical

Principles in Astrophysics and Rela`i ity, Chicago, May 27, 1'.75 ABSTRACT

It is likely that supermassive black holes (M - 10 6 to 1010

M0 ) exist in the nuclei of many quasars and galaxies. The collapse which forms these holes and subsequent collisions between them should produce strong, broad-hand bursts of gravitational waves: for a source of mass M at the Hubble distance of 10 10 light years, the dimensionless ampli'.ude would be h . 2 x 10-17 x

(M/10 6 M0 ), and the duration of the burst would be T - ( 90 sec)x

(M/10 6 M0 ). Such bursts might arrive at Earth as often as SO

times per year--or as rarely as once each 300 years. The detection of such bursts may be possible within the next few years using dual-frequency doppler tracking of interplanetary spacecraft.

Subjec t headings: galactic. nuclei - gravitation - quasistellar

sources or objects - relativity

i 1. SOURCES OF THE BURSTS

When building models for the cores of quasars, of strong radio sources, and

of active galactic nuclei, theorists typically conclude that, whatever may be

in the core, it is likely to generate one or more supermassive black holes 10 (M 10 6 to 10 MQ ) in a time short compared to the age of the Universe. See,

e.g., Lynden-Bell (1969), Wolfe and Burbidge (1!'70), Spitzer (1971), and Saslaw

(1974, 1975).

A typical scenario involves the collapse of supermassive stars, gas clouds, or star clusters to form holes, and perhaps subsequent collisions between holes.

Each such collapse or collision involving masses M z! 10 6 Ma should produce a burst of gravitational radiation so strong, that it might be observable at Earth.

However, in the alternative scenario of a single hole which forms small (M <<

10 (' MO ) and then grows by gradual accretion, no strong burst of gravitational waves can be expected (Davis et al. 1971).

There are so few quasars and galaxies in the Universe (- 10 t0 ), and each one can produce so few strong gravitational-wave bursts (perhaps ; 10) that

to detec, several bursts per year, we must search for them Over the entire volume of the observable Universe. Most such bursts will probably come from a redshift

z = 2.5, when the Universe was about 2 billion years old, since quasar activity

seems to have peaked very sharply at that time (Schmidt 1970, 1972).

II. MEAN TIME BETWEEN 13URSTS

Tlie mean time At between such gravitational-wave bursts at Earth can be

expressed in terms of: (i) the Hubble expansion rate and deceleration parameter 11 q of the Universe today (which we assume globally Friedmann with zero cosmological u

constant); (ii) the redshift z = 2.5 at which most of the bursts were generated;

(iii) the number density n o today of "centers" where bursts or'.ginated (each

1 center was probably a galactic nucleus); (iv) the mean number of bursts N generated in each center during its active life; and (v) the speed of light c:

1 [ 1 - q 0 + q 0 z - (1-q 0 )(1 + 2g0z)1/2J At R 4nR 2 n 0 Nc (H0/c)go2',1 + z) cf. equation (29.33)of Misner, Thorne, and Wheeler (1973)--cited henceforth as MI V.

Becau-ie number densities of cosmological objects are usually computed using

11 0 - 100 km sec -1 Mpc -1 and q o - 1, we shall assume these parameters; throughout.

The more modern values H o - 55 and q o << 0.5 (Sandage 1972; Gunn et al. 1974) would give values of At smaller by a factor of 3. With H 0 = 100, q o = 1, r - 'I.5 the time between bursts is

At = (0.06 years) (n0/Mpc-3)-I N-1 (2)

Various assumptions--each quite reasonabl y --lead to widely differing estimates of n 09 the density of burst centers. If nearly every quasar (radio-quiet or radio-loud) produced at ..east one black hole and accompanying burst, then n o is the density of dead quasars in the Universe: I

1 x ].0 -6 ^ 1 5,^ 0.8 x 10 -4 t _ t0 n liv4 (t) _ t^, o "( 10 dT - f P,3 Mpc3 tlife n0 p t life dt tlife M c3 ) 1

Here (t) is the comoving density of live quasars at time t with M V < -22 nlive as estimated by Schmidt (1970, 1972); is the mean lifetime of quasar activity tlife in each center; and t o is the present age of the Universe. Schmidt's evolution 5t/t it-5t/to law, 1 live °` 10 0 = C requires an upper limit tlife < t0/11.5; and a lower limit might be (typical size, 100 kpc, of extended radio-emitting t,JLife ' regions)/(typical velocity, U.i c, expected for expan::on of extended regions in models of radio sources) ` 3 x 106 yrs (cf. Longair, Kyle, and Scheuer 1973;

Blandford and Rees 1974). 'Thus

1 x 10-3 Mpc -3 < n 0 5 0.2 Mpc -3 if all quasars wete bu r st centers. (3) Suppose, alternatively, that all galaxies with violently active nuclei produce

supermassive holes and wave bursts during their violence. Presumably the violence

seen in strong r;% dio galaxies is sufficient. This leads to an n roughly the U - same as for quasars (eq. [31) (Schmidt 1966, 1972).

Presumably the violence of a Seyfert galaxy also qualifies. The number density of Seyferts active today is - 2 x 10 -4 Mpc -3 (Huchra and Sargent 1973 adjusted

from If - 75 ► ) H o = 100). However, it is likely that Seyfert acti%ity is transient, and that in the past a large fraction of all spiral galaxies with M V < -19 experienced nuclear violence comparable to that in Seyferts (n 0.01 Mpc -3 ; Shapiro 1971). 0 - Arguments for such widespread violence in spirals include these: (i) Of all non-Virgo-cluster and non-local-group spiral galaxies with corrected recession velocities v < 1000 km/sec, - 10 per cent have small radio sources in their nuclei, and - 5 per cent are "optically active" in ways that could be remnants of earlier, more violent behavior (Ulrich 1974). (ii) The only big (M V < -19) spirals close enough to be studied from the ground with optical resolution < 10 pc are our galaxy and M31 (Andromeda); and they both exhibit peculiar nuclear activity: (a) both show radial gas outflows suggestive of violent nuclear explusions in the past, perhaps 10 5 years ago (Munch 1960, Rubin and Cord 1969, Sanders and Prendergast

1974, and references therein); (b) M31, as viewed by Stratoscope II (Light,

Danielsen, and Schwarzszhild 1974), has a nucleus so compact (M - 5 x 10 7 M; scale

height 0.5 pc) that all of its stars more massive than 2 MO may by now have sunk

to the center, producing violence (cf. Spitzer and Schull 1975); (c) the central

3 pc of our own galactic nucleus contains a radio source with diameter 5 200 AU and luminosity = 10 33 erg/sec at v - 10 GHz (Lo et al. 1975), which coincides with a discrete near-infrared source (Becklin and Neugebauer 1975 source 16) that

does not show CO absorption (Becklin, private communication) and that therefore

could be a cluster of red dwarfs emitting Ltotal 10' L0 and congregating around

3 a supermassive black hole (Sanders and Lowinger 1.972); (d) one cannot rule out our nucleus containing a black hole of mass as large as 1 x 10 8 M0 (Sanders and Wrixon 1973).

If, as suggested by these observations, most spiral galaxies in the Universe

Have experienced enough nuclear violence in the past to produce supermassive holes and strung gravitational-wave bursts, n o may he as loge as 0.31 Mpc -3 . If dwarf spirals (M > -19) also contain holes, but show little nuclear activity now V because of a paucity of gas to accrete into the holes, then n o could be 0.3 Mpc-3.

On the other hand, if the only burst centers were the currently active Seyferts, then no - 2 x 10 -4 . Thus,

-4 2 x 10 Mpc -3 n s 0.3 Mpc '3 if galaxy nuclei art, burst centers. (4)

Note the strikin gg resemblance of equationq (4) to equationq (3)--a resemblance which suggests to Lynden-Bell (1969) that most galaxies were quasars at one time and now contain supermassive holes.

The average number of strong gravitational-wave bursts from each burst

center is not likely to he large, perhaps

1 < N 5 10, (5) because the gravitational and collisional effects of each massive object are

likely to inhibit the formation and evolution-to-collapse of other massive objects.

However, our ignorance here, like our ignorance of n o , is enormous.

By combining equations (2) - (4) we arrive at a range of "reasonable values"

for the time between gravitational -wave bursts at Earth

1 week 4 At 5 300 years. (6)

However, we must admit that hardly any strong bursts at all (At >> 300 years) is

also reasonable; holes might usually form small and grow by gradual accretion.

4 III. EXPECTED CHARACTERISTICS OF THF. 11URSTS

Consider the collapse of a massive star or star cluster to form a black hole, or the collision be tween twc, black holes with impact parameter of the order of their size. Let tits., total mass Involved be M and let the total energy radiated as gravitational waves be EMc 2 . (A reasonable efficiency is c - 0.1)

Most of the gravitatian-31 waves will come off in a burst with timescale 3r3 (;M/, at the source (see, e.g., Press 1971), and redshifted timescale at Earth

T : OvI CM/c 3 ) (1+z) - (90 see) (M/106 M0 ) if z - 2.5. (7)

The polarization-averaged dimensionless amplitude (h) = (1)Tij hij /4) 1/2 of the waves at Earth can be computed fr

3 2 c (h2 (e Mc 2) (total energy radiated) = (4nR2)T (1-1 2) (A) $ 71C z energy flux ), area duration (blue - at Earth (around source) x ^of burst)xif0 sh see equation (35.23) of MTW. Hera R is as in equation (1). For H 0 = 100, q 0 = 1, z = 2.5 this gives

-17 1/2 (h) = (6 053 f) 1/ ` CM/Rc 2 = 2 x 10 (e/0.1) (M/10 6 MO ). (9)

Table 1 shows the expected (h) and t for sources if different mass M.

By observat-ional studies of wave forms h(t) one may deduce much about the details of sources. For example: (i) If h(t) returns to its initial value after the burst, hinitial' then the source involved only one object (e.g., h final a single star or star cluster which collapsed to form a hole); but if h final # llinirial' then the source involved two or more discrete objects (e.g., two black holes that collided and coalesr-d). (ii) If part or all of the burst is a rather monochromatic, sinusoidal signal, then the source may have been a rapidly rotating, relativistic star which went unstable by the "Ch.indrasekhar-Dedekind

5 bar-mode process" (Chandrasekhat 1970). (iii) If part or all of the burst involves a rather sinusoidal signal with a variety of harmonics present, then the source may have been a rapidly rotating, highly relativistic star which went unstable by the "Friedtnin (1975) ergotoroid process". (iv) If the burst is entirely broad-band, except for a rapidly damped riny'.ng at the end, the source may have been a star that encounte • ed a "dynamical instability" (see, e.g., Friedman and

Schutz 1975), and collapsed to form a black hole.

I%. DETECTION OF 01F. BURSTS BY DOPPLER TKACKING OF SPACECRAFT

In Lhe next few vears the best detector for the gravitational-wave bursts of Table 1 will probably be doppler tracking of one or more distant interplanetary spacecraft: A tracking station on Earth transmits monochromatic electromagnetic waves with frequency locked onto a highly stable clock (master oscillator). The spacecraft receives the waves, amplifies them, and transmits them back to Earth

(i.e., it "transponds" them). The tracking antenna at Earth receives the transponded waves, compares them with the transmitted waves by counting the number of cycles and fractions thereof during an integration time a , a derives a tint' frequency shift from the comparison. (For further detail see, e. , ., Anderson

1973). The measured frequency shift is due primarily to the ve city of the spacecraft relative to Earth (doppler shift), but it also contains contributions

("noise") from frequency fluctuations and drift of the master oscillator, from time-varying dispersion of the electromagnetic waves in the Earth's ionosphere and troposphere and in the interplanetary median, and from passing gravitati,-)nal waves.

111e gravitational-wave contribution as computed by F.stabrook and Wahlquist

(1975) can be described as follow ,,. Orient the spatial axes of a Euclidean coordinate system so the gravitational waves travel in the z direction, and the

Earth-spacecraft line of sight has length R and lies in the x-z plane at an angle

6 s T

0 relative to the z axis. Tlien the component of the gravitational waves which

influences the doppler signal is hTT h(t - z). [For the meaning of h T` see xx xx chapter 35 of M114.1 1'he influence of It on the doppler signal is given by

Av /1 - cos 0 1 + cos 0 v 2 — h R -cos 0 h T + 4 -- 1 I h E (10)

(Estabrook and Wahlquist 1975). Here Av/v is the frequency shift of a specific

short piece of the electromagnetic wave train--a piece received at Earth at

time t R ; and h E , h 'r$ h are the values of It encountered by that same piece of

wave train at its moments cf emission, transponding, and reception:

h F = h(t R - 20 , h ` - h (t K - E[1 + cos 01), li lt h(t R ). (11)

1Wo features of equation (10) are important: First, the magnitude of the

gravitational-wave-induced frequency shift is Av /v - h; second, (as Estabrook

and Wahlyuist emphasize) the grivitational waive-form is repeated three times in

the Doppler signal, with relative amplitudes and time separations that depend

on only one unknown parameter: the angle 0. 'Mis second feature may allow one

to extract gravitational-wave effects in the presence of much larger doppler

noise, and may also allow one to determine the angle 0. By simultaneous tracking

of several spacecraft one could dig even deeper into the noise, and/or one could

determine the 2-dimensictal direction of the source.

When using single-frequency radio waves ("S-band", A = 14 cm), the NASA

deep-space network can track spacecraft under favorable conditions (no planet

or sun or high-density plasma cloud in the radio beam) with rms doppler residuals

of 1

I Our remarks herd and below about NASA doppler capabilities and possible improve-

ments are b. _d largely on discussions with JP1, personnel, including John D.

Anderson, Richard Davies, Frank B. Estabrook, Richard Svdnor, Oldwig H. Vonroos,

uid liriant Winn.

7 A(Av/v) v (3 x 10-13 ) for t int 2 7 min, (12)

where tint is the integration time. This precision is far short of that required

for detection of the wave bursts shown in Table i, [d(Av/v) = h - 10 -14 to 10- 17

However--and this is the key point--there has riot been much motivation for

Improvements in doppler tracking in recen t years. Given the motivation, cne

could improve on the present precision by several irders of magnitude.

The following improvements, largely motivated by non-doppler con3iderations,

:ire underway or could be Lr. ^lcnented with small effort and cost: (i) conversion

from s ligle-frequency tracking to dual-frequency ("S-band" from Earth to Space-

c• r.if t ["tip ► ink" J ; "S- band" and "X-hand" [ ^ = 3.6 c • m l from spacecraft to Earth

["downlink"j; conversion recently completed); (ii) replacement of rubidium clocks

by hydrogen-maser crocks as the master oscillators (replacement to be complete

by stammer 1976); and (iii) replacement of the present "doppler extractor," which

Is accurate to 10 -2 cycles, by a new extractor accurate to 10 -3 cycles (replacement

not now planned, but easily doable and defin'tcly needed for the doppler system

to take full advantage of the new master oscillators). With these improvements

the system residuals could drop as low as d(Av/v) - 2 X 10 -15 for t int z 15 niin--

though dispersion of the signal, even with dual-frequency monitoring, may make

the overall residuals somewhat worse than this. By using the triplet structure

of the gravitational-wave signal to dig Ato the noise, and by transpunding off

spacecraft more distant than about 10 A.U., one might be able to detect

-15r waves with 11 1 . 10 and i - 711 m:n (case II of Table 1). NASA could

try this in late !976 with Pioneer 10 and 11 (the two spacecraft which flew by

Jupiter in 1973-74); though such an experiment will be degraded by the lack of

dual-frequency capabilities in tho Pioneer spacecraft. NASA could also try with

the ^Viriner Jupiter-Saturn mission (1977 launch; .Jupiter flyby in 1979).

R • ------TT T

Further doppler improvement: might produce a capability for detect trig case-III waves (h - 1 x 10 -16 , t - 7 min) and conceivably case-IV by late in this decade or early in the next. (For such waves one can use any spacecraft more distant than 1 A.U.--i.e., almost anv interplanetary spacecraft at all).

Among the possible improvements are: (i) X-band tracking on uplink as well as downlink (work on this begins in 1978); (ii) replacement of hydrogen-maser master oscillators by superconducting-cavity stabilized oscillators, which in 1974 had

-16 a stability 6(Av/v) - 6 x 10 for t 10 sec (Stein and Turneaure 1975), int -t6 which will probably reach 6(Av/v) = 1 x 10 in 1976 (Turneaure, private communication), and which--using niobium-coated sapphire cavities--may ultimately achieve

tabilities much higher than 1 x 10 -16 (B : , Insky and Manukin 1974); (iii) the design and construction of new tracking-station electronics (doppler extractors, receivers, etc.) to go along with the improved master oscillators.

Buffeting of the spacecraft by f l uctuating solar radiation pressure and solar wind will hide the gravitational -wave signals at some level (perhaps below case III?) despite their unique triplet structure. If necessary, one can reduce buffeting by using a drag-free ("conscience-guided") spacecraft (Kundt 1974) or a twin-probe spacecraft (Bertotti and Columbo 1972). The TRIAD drag-free s pace- craft, which has already been developed, constructed, and flown once (.Johns Hopkins and Stanford 1974) is sufficiently drag free (a < 5 x 10 -9 cm/sec t ) to reduce time-averaged buffeting noise to 6(Av/v) 1 x 10-17 (tint /I min)--a noise level

M comparable to the gravitational-wave signals of Table 1. However, the TRIAD

"dead band" (maximum 2at 2 displacement between firings of correction Jets) was 1 millimeter--too large for gravitational-wave detection. A dead band of 0.1 y would be needed to completely prevent buffeting at the level of case-IV wave bursts.

A twin-probe spacecraft is not subject to such dead-band limitations.

i I I 1_ ,

Time-varying dispersion cinnLL be completely compensated for by dual-

frequency ranging. One might ultimately remove dispersion in the Earth'e atmosphere

and near the Earth, as well as all noise sources at the tracking station (e.g.,

fluctuations in antennrc dimensions), by tracking two spacecraft at different

distances (e.g., 1 A.U. and 10 A.U.) but in the same line of sight, and by differ-

encing their doppler signal p (Davies 1974). And someday one might remove dispersion

altogether by tracking at optical frequencies.

Q^e might he :.ole to search for case-I1 and case-III bursts without the

enormous expense of special-purpose spacecraft (drag-free, twin-probe, or two-

in-lane-of-sight). Detailed studies are needed to determine this.

Simultaneous with any search for such gravitational-wave bursts one should

also watch for associated electromagnetic events (radio, infrared, optical, or

X-ray) and for possible redshift changes due to mass outflow in gravitational

waves. 'llte electromagnetic flux at Earth and apparent bolometric magnitude would be

F = (0.,3 erg a--m -^k to - 2.5 log — em &W (13) 2 /t BOL "- 10 i /T cm sec ► em t;w em gw `

11ie duration of the electromagnetic event, T em , should be much longer than that

of the gravitational-wave burst, T gw , because of absorption and reemission by

gas surrounding the hole. The electromagnetic energy, might be far less Eem'

than the gravitational energy, Egw--or they might be comparable.

Even if the gravitational waves of Table 1 do not exist, doppler tracking

should ultimately reveal waves at h - 10 -19 due to (i) close binary systems in

our galaxy; (ii) the collapse of normal. stars (M <100 M ai ) to form black holes in

nearbv galaxies (distance < 10 Mpc); (iii) the capture of globular clusters,

containing black holes of 10 3 - 10 4 Mtn , by galactic nuclei at a distance -1000

Mpc, followed by collisions and coalescences of the holes in the nuclei (cf.

Kahcall and ostriker 1975; Silk and Arons 1975; Tremaine, Ost r iker, and Spitzer

10 1975); and/or near encounters between compact stars in a possible dense star cluster in the nucleus of our own galaxy (7.e1'dovich and Polnarev 1974). In the case of close binary systems the periodicity of the sig-ral can be used to enhance the accuracy of the experiment to an effective level of h - 10 -18 (Daviets 1974,

Estabrook and Wahlquist 1975).

V. SUGGESTIONS FOR FURTHER STUDY

In view of the above discussion, we suggest the following: (1) That space- research organizations (NASA, USSR Academy of Sciences, ESRO) initiate detailed studies of the expected limits which various doppler-tracking configurations can place on gravitational waves of the type shown In Table 1. (2) That, if those

:studies are as optimist i c as our cursory analysis, high priority be given to doppler-tracking se , . iivs for gravitational-wave bursts. (3) That astronomers and astr,poysicists try to firm up our estimates of the density n of centers 0 where strong wave bursts were generated, and of the number N of bursts per center.

(4) That relativity theorists develop a catalog of gravitational wave forms to be expected from the various objects and events that might occur In the nuclei of galaxies and quasar -c. (5) "lliat experimenters try to develop alternative detection schemes for they waves shown in Table 1.

For helpful discussions or correspondence we thank the JPL personnel listed in footnote 1; also Eric Becklin, Peter Bender, Bruno Bertotti, Daniel de Bra,

Peter Goldreich, Wo;fgang Kundi, Charles Misner, Gerry Neugehauer, Jerry Ostriker,

Wallace Sargent, Bill Saslaw, Maarten Schmidt, Lyman Spitzer, John Turneaure, and To-.y Tyson. one of us (KST) thanks the Aspen Center for Physics for hospitality during part of this research.

11 111W --1 1 ,.MIM. q

TABLE. I

CIIAHACTE.RISTICS OF GRAVITATIONAL-WAVE. BURSTS FROM BLACK-HOLE EVENTS

INVOLVING A MASS M AT A REUSHIET z - 2.5

Case I Case II Case III Case IV

Na g s, M 5 x 108 DINS 5 x 10 7 Mhl 5 x 10 6 MCA 5 x 10 5 r,^ 1 x 10-15 1 x 10 -16 1 x 10-1.7 Wa y .- :amplitude, h I x 10-14

Burst duration, i 700 min. 70 m.n. 7 min. 40 eic.

6&-- REFERENCES

Anderson, J. 1). 1973, in B. Bertotti, ed., Experiment__

.Academic Press), p. 163.

Baiicall, J. N. and Ostriker, J. P. 1975, Nature, 23.

Becklin, E. E. and Neugebauer. C. 1975, q.._ J._ (Letters)_, 200, 1.71.

Bertotti, B. rtnd Colombo, G. 1972, Ap._and Space Sci., 17, 223.

Blandford, R. D. and Rees, M. J. 1974, M.N. R.A.S., 169, 395.

Braginsky, V. B. and Manakin, A. B. Measurement of Small Forces in Pgy!sics

Experiments (Moscow: Nauka), p. 127; English translation by 0. Ch;cago

Press, in preparation.

Chandrasekhar, S. 1970, Phys _Rev. Letters, 24, 611.

Davies, R. W. 1974, in Ondes et Radiations ^,ravitionelles (Faris: Editions de

C.N.R.S.), p. 33.

Davis, M., Ruff ini, R., Press, W. II., and Prise, P. H. 1971, Phys. Rev. Letters,

27, 1466.

Estabrook, F. B. and Wahlquist, H. 1). 1975, Gen. Rel. Gra y ., in press.

Friedman, J. L. 1975, paper in preparation.

Frie iwin, .1. L. and Schutz, B. F. 1975, AL J., in press.

(:win, J. E. , ( got I, J. R., ScIirarim, I). N., rind Tins Iey, 11. M. 1974, A J.,

' y/j, 51,3.

Huchra, J. and Sargent, W. L. W. 1973, Ap. J., 186, 433.

Johns Hopkins University, Staff of the Space Science Department of the Applied

Physics Laboratory, and Stanford University, °taff of the Guidance and

Con troI Laboratory 1974, J. Spacecraft, II, 637.

13 1_ l 1 I L.

Kundt, W. 1974, Ap._ & Space Sci., 30, 455.

Light, E. S., Danielsen, R. F.., and Schwarzschild, M. 1974, ^6L). .1._, 194, 257.

Lo, K. Y., Schilizzi, R. T., Cohen, M. H., and Ross, H. N. 1975, Ap. J. (Letters),

In press.

Longair, M. S., Ryle, M., and Scheuer, 1. A. C. 1973, M.N.R.A.S., 164, 243.

Lynden- Bell , D. 1969, Nature ,223, 690

Misner, C. W., Thorne, K. S., and Wheeler, J. A. 1973, Gravitation (San

Francisco: W. H. Freeman and Co.); cited in text as MTW.

Munch, G. 1960, !Np. 131, 250.

Press, W. 11. 1971, Ap. J. (Letter, 170, L105

Rubin, V. C. and Ford, W. K. 1969, Ap.. J_. , 159, 379.

Sandagv, A. 1972, l uart-. J.R.A,S._, 13, 282.

Sanders, R. H. and Lowinger, T. 1972, A. J., 77, 292.

Sanders, R. H. and Prendergast, K. H. 1974, Ap. J., 188, 489.

Sanders, R. 11. and Wrixon, G. T. 1973, Astron. and Ap., 26, 365.

Saslaw, W. C. 1974, in J. R. Shakeshaft, ed., The Formation and Dynamics of

Galaxies, Proceedings oI I.A.II. Symposium No. 58 (Dortrecht -Holland: Reidel),

p. 305.

1975, in A. Hayli, ed., lnamics of Stellar Systems,tems, Proceedings

of I.A.U. Symposium No. 59 (Dortrecht-Holland: Reidel), p. 379.

Schmidt, M. 1966, Ap. J. _, 146, 7.

1970, Ap. J., 162, 371.

1972, Ap. J., 176, 303.

Shapiro, S. L. 1971, A. J., 76, 291.

Silk, J. and Arons, J. 1975, Ap J. (Letters), 200, L131.

Spitzer, L., Jr. 1971, in Semain d'etude sur les noyeaux des galaxies,

Pontificae Academiae Scientarum, Script Varia no. 35, p. 443.

14 4

Spitzer, 1.., Jr., and Schull,J. M. 1975, Ap. J., in press.

Stein, S. R. and Turneaure, J. P. 1975, IEEE Proceedings, in press.

Tremaine, S. D., Ostriker, J. P., and Spitzer, L., Jr. 1975, Ap. J., 196, 407.

Ulrich, M.-H. 1974, in J. R. Shakeshaft, ed., The Formation and Dynamics of

Galaxies, Proceedings of I.A.U. Symposium No. 58 (Dortrecht-Holland: Reidel),

p. 279.

Wolfe, A. M. crud Kurhidge, G. R. 1970, Ap. J., 161, 41Q.

Lel'dovich, Ya. 11. and Polnarev, A. G. 1974, Soviet Astron. - AJ, 18, 17.